Advertisements
Advertisements
Question
Solve the following by reducing them to quadratic equations:
x4 - 26x2 + 25 = 0
Solution
Given x4 - 26x2 + 25 = 0
Putting x2 = y, the given equation reduces to the form y2 - 26y + 25 = 0
⇒ y2 - 25y - y + 25 = 0
⇒ y(y - 25) -1(y- 25) = 0
⇒ (y - 25) (y - 1) = 0
⇒ y - 25 = 0 or y - 1 = 0
⇒ y = 25 or y = 1
∴ x2 = 25
⇒ x = ± 5
or
x2 = 1
x = ±1
Hence, the required roots are ±5, ±1.
APPEARS IN
RELATED QUESTIONS
Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(4 - k)x2 + (2k + 4)x + 8k + 1 = 0
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
For what value of k, the roots of the equation x2 + 4x + k = 0 are real?
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
If α and β are the roots of the equation 2x2 – 3x – 6 = 0. The equation whose roots are `1/α` and `1/β` is:
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x + 1)(x – 2) + x = 0
If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is ______.
